128
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Apolarity, Hessian and Macaulay Polynomials

&
Pages 226-237 | Received 07 Mar 2011, Published online: 04 Jan 2013

REFERENCES

  • Alexander , J. , Hirschowitz , A. ( 1995 ). Polynomial interpolation in several variables . J. Algebraic Geom. 4 ( 2 ): 201 – 222 .
  • Ciliberto , C. , Russo , F. , Simis , A. ( 2008 ). Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian . Adv. Math. 218 ( 6 ): 1759 – 1805 .
  • CoCoATeam. CoCoA: A system for doing Computations in Commutative Algebra. Available at http://cocoa.dima.unige.it. Last accessed October 3, 2012 .
  • Cox , D. A. ( 1987 ). Generic Torelli and infinitesimal variation of Hodge structure. In Algebraic Geometry, Bowdoin, 1985 (Brunswick, Maine, 1985). Vol. 46. of Proc. Sympos. Pure Math., Amer. Math. Soc., Providence, RI, pp. 235–246 .
  • Dolgachev , I. , Kanev , V. ( 1993 ). Polar covariants of plane cubics and quartics . Adv. Math. 98 ( 2 ): 216 – 301 .
  • Dolgachev , I. V. ( 2010 ). Topics in Classical Algebraic Geometry. Preprint. Available at http://www.math.lsa.umich.edu/ ∼idolga/CAG.pdf. Last accessed October 3, 2012 .
  • Eisenbud , D. ( 1995 ). Commutative Algebra . Vol. 150 of Graduate Texts in Mathematics . New York : Springer-Verlag, With a view toward algebraic geometry .
  • Geramita , A. V. ( 1996 ). Inverse systems of fat points: Waring's problem, secant varieties of Veronese varieties and parameter spaces for Gorenstein ideals . In: The Curves Seminar at Queen's, Vol. X (Kingston, ON, 1995) . Vol. 102 of Queen's Papers in Pure and Appl. Math. , Kingston , ON : Queen's Univ , pp. 2 – 114 .
  • Iarrobino , A. , Kanev , V. ( 1999 ). Power Sums, Gorenstein Algebras, and Determinantal Loci . Vol. 1721 of Lecture Notes in Mathematics . Berlin : Springer-Verlag, Appendix C by Iarrobino and Steven L. Kleiman .
  • Iliev , A. , Ranestad , K. ( 2001 ). Canonical curves and varieties of sums of powers of cubic polynomials . J. Algebra 246 ( 1 ): 385 – 393 .
  • Iliev , A. , Ranestad , K. ( 2001 ). K3 surfaces of genus 8 and varieties of sums of powers of cubic fourfolds . Trans. Amer. Math. Soc. 353 ( 42 ): 1455 – 1468 .
  • Macaulay , F. S. ( 1994 ). The Algebraic Theory of Modular Systems . Cambridge Mathematical Library. Cambridge : Cambridge University Press, Revised reprint of the 1916 original, With an introduction by Paul Roberts .
  • Ranestad , K. , Schreyer , F.-O. ( 2000 ). Varieties of sums of powers . J. Reine Angew. Math. 525 : 147 – 181 .
  • Reichstein , B. , Reichstein , Z. ( 1993 ). Surfaces parameterizing Waring presentations of smooth plane cubics . Michigan Math. J. 40 ( 1 ): 95 – 118 .
  • Communicated by C. Pedrini.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.